On the partitioned matrix O A A * Q and its associated system A X = T , A * Y + Q X = Z
RAIRO. Analyse numérique, Tome 15 (1981) no. 2, pp. 177-184. 
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     author = {Valerio, Vladimiro},
     title = {On the partitioned matrix $\begin{pmatrix}O&A\\A^\ast &Q\end{pmatrix}$ and its associated system $AX=T, A^\ast Y+QX = Z$},
     journal = {RAIRO. Analyse num\'erique},
     pages = {177--184},
     publisher = {Centrale des revues, Dunod-Gauthier-Villars},
     address = {Montreuil},
     volume = {15},
     number = {2},
     year = {1981},
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Valerio, Vladimiro. On the partitioned matrix $\begin{pmatrix}O&A\\A^\ast &Q\end{pmatrix}$ and its associated system $AX=T, A^\ast Y+QX = Z$. RAIRO. Analyse numérique, Tome 15 (1981) no. 2, pp. 177-184. http://archive.numdam.org/item/M2AN_1981__15_2_177_0/

1 A Ben-Israel, A note on partitioned matrix equations SIAM Rev , 11 (1969), 247-250 | MR | Zbl

2 A Ben-Israel, Generalized inverses theory and applications J Wiley and Sons (1974), New York | MR | Zbl

3 P Bhimasankaram, On generalized inverse of partitioned matrices, Sankhya, Ser A, 33 (1971), 311-314 | Zbl

4 A Bjerhammar, Theory of errors and generalized inverse matrix Elsevir Scien Public Co (1973)

5 T Boullion, P L Odell, Generalized inverse matrices J Wiley and Sons (1971), New York | Zbl

6 F Burns, D Carlson, E Haynsworth, T Markham, A generalized inverse formula using the Schur complement, SIAM J , 26, (1974), 254-259 | MR

7 D Carlson, E Haynsworth, T Markham, A generalization of the Schur complement by means of the Moore-Penrose Inverse SIAM J Appl Math 26 (1974), 169-175 | MR | Zbl

8 Ching-Hsiang Hung, T Markham, The Moore-Penrose inverse of a partitioned matrix M=ACBD Linear Alg and its Appl , 11 (1975), 73-86 | MR | Zbl

9 R E Cline, Representation for the generalized inverse of partitioned matrix SIAM J Appl Math , 12 (1964), 588-600 | MR | Zbl

10 R E Cline, Representation of generalized inverse of sums of matrices SIAM J Num Anal , Ser B, 2 (1965), 99-114 | Zbl

11 R W Cottle, Manifestation of the Schur complement Linear Alg and its Appl , 8 (1974), 189-211 | Zbl

12 T N E Greville, Some applications of the pseudo-inverse of a matrix SIAM Rev , 2 (1960), 15-22

13 C Hadley, Linear Algebra Addison-Wesley (1965), New York

14 G Marsaglia, G P H Styan, Rank conditions for generalized inverses of partitioned matrices Sankhya, Ser A (1974), 437-442 | MR | Zbl

15 G Marsaglia, Equations and inequalities for ranks of matrices Linear and Multil Alg , 2 (1974), 269-292 | Zbl

16 S K Mitra, P Bimasankharam, Generalized inverse of partitioned matrices and recalculation of least squares estimates for data or model charges Sankhya, Ser A, 33 (1971), 395-410 | MR | Zbl

17 S K Mitra, Fixed rank solutions of linear matrix equations Sankhya, Ser A, 34 (1971) 387-392 | MR | Zbl

18 C R Rao, Calculus of generalized inverses of matrices, Part I General Theory Sankhya, Ser A , 29 (1971), 317-342 | Zbl

19 C R Rao, S K Mitra, Generalized inverse of matrix and its application J Wiley and Sons (1971), New York

20 C H Rohde, Generalized inverse of partitioned matrices SIAM J , 13 (1965), 1033-1035 | MR | Zbl

21 V Valerio, Sulle inverse generalizzate e sulla soluzione di particolari sistemi di equazioni lineari, con applicazione al calcolo delle strutture reticolari Ace Naz Lincei, Rend sc , vol LX (1976), 84-89 | MR | Zbl

22 V Valerio, On the reticulated structures calculation Seminar held at the Delhi Campus of the Indian Statistical Institute (Nov 1977) unpublished communication, to appear